Problem with curve modifier on zipper
(Creator of the tutorial here)

One of the curve handles of the curve that deforms the plane is pointing the wrong way, causing part of the mesh to be flipped upside down, as shown below by the directional arrows of the curve:




Enter 'Edit mode' for curve (Bezier Curve.001).
Select the middle curve point, which is the one that is flipped.
Rotate the curve point 180 degrees on the 'x' axis (R,X,1,8,0)
Exit edit mode, and if the error hasn't gone, simply turn the curve modifier on and then off and the mesh should refresh.